I have a modest spoiler so don't read below if you care about the content of the curriculum at Vulcan Junior High.
Ok, not to give anything away in the movie, but in an early sequence where the various Vulcan kids are being tested on all kinds of knowledge--math, biology, physics, etc--there was one clear social science reference--non-rivalry & non-excludability. These are the defining characteristics of Public Goods, and are central concepts in Mancur Olson's classic Logic of Collective Action. Olson famously (famous enough to make it into the 23rd century and all the way to Vulcan) argues that it will be difficult to cooperate to provide Public Goods--when one's usage of a good does not reduce its availability for others and where non-contributors cannot be excluded. In such cases, free-riding is not only likely but the logical course of action.
Olson's insights here, while often contested, have shaped how we think about political mobilization, the need for government/coercion, and especially the environment. Why recycle? If I do it and no one else does, my effort is wasted. If everyone does it but I do not, then the planet is clean and my marginal waste is irrelevant.
It is especially ironic that Public Goods appears in the new (and rockin') Star Trek because the logic of collective action largely produces a pessimistic, cynical outlook towards human nature and the possibility of cooperation but ST is all about an optimistic vision of the future. Perhaps the new writers of ST mythology, JJ Abrams and the gang, are trying to square the geek circle--that we can overcome the collective action problem and that we will so that we get this amazing future of the Federation of Planets, in which Starfleet is explicitly referred as a force for humanitarian efforts and peacekeeping. Indeed, for a minute, it sounded like the conventional perception of the mission of the Canadian Forces before Operation Medusa in Afghanistan in 2006 (first major combat for Canada since the Korean War).
Of course, Olson and his successors provide a variety of ways out of the collective action problem: small groups can mobilize as their members perceive their contributions as mattering; individual entrepreneurs can see it in their interests to facilitate and even underwrite cooperation; and the like.
To sum up, it was just a fun movie that made a very interesting and deliberate reference that is far more intriguing to me than the volume of a cylinder--another example in that sequence in the movie. This is not the first time that Star Trek has overlapped with social science, and it will almost certainly not be the last, given the box office success it is having. Live long and prosper, indeed.